This invention relates to limited-angle image reconstruction and more particularly to a method to estimate the exterior boundary of an object and its use in limited-angle computerized tomography.
In some x-ray CT situations the x-ray data of the object is available only in a limited angular range. Limited-angle imaging occurs, for example, when scanning in some angular range is obstructed by other physical objects, or when the x-ray is attenuated too much in some angular range to serve any useful purpose. Under such circumstances limited-angle reconstruction techniques could be employed to reconstruct the object from x-ray data and other information about the object, such as: (1) exterior boundary of the object; (2) upper bound of the object density; and (3) lower bound of the object density. It has been shown that by using this information in addition to the limited-angle x-ray data, the object may be reconstructed uniquely; refer to Tam, K.C. and Perez-Mendez, V., J. Opt. Soc. Am., 71 (1981) 582-592. One limited-angle reconstruction algorithm developed in this reference is shown in FIG. 1; the image is transformed back and forth between the object space by filtered back-projection, and the projection space by projection, being corrected by the a priori information in the object space, and the limited-angle known projections in the projection space.
The upper and lower bounds of the object density are usually available. For example, they can be estimated from the a priori knowledge about the composition of the object; in fact the lower bound is usually taken to be zero. Currently there is no systematic method to obtain the object boundary. In the literature it is simply assumed the object boundary can be estimated one way or another. Some of the methods mentioned include probing, modeling, etc., which all involve additional equipment and which may not yield the boundary of the object actually imaged.
The inventor's copending application Ser. No. 877,083, filed June 23, 1986, "Method for Reconstructing Objects from Limited-Angle Scannings in Computerized Tomography", now abandoned, and continuation application Ser. No. 205,398, filed June 10, 1988, relates to an object to be imaged which contains a medium that occupies most of the cross-sectional area and the density of the medium is usually known, for instance a metal medium with embedded flaws. Under these circumstances image reconstruction of the flaw is improved by constructing a flaw-enclosing region; since knowledge of the region of occurrence of the flaw is more precise, using the flaw-enclosing region as a priori information yields better results than if the much larger object boundary were used. This method assumes the boundary of the object is known exactly.